While every point in the FITS data array can be located
in the cooordinate system determined by the array axes, scientific interpretation
requires knowledge of the physical or world coordinates corresponding to the index
points. For example, in an array that represents a spectrum, the relation between
wavelength and index number on the wavelength axis must be known. The original
FITS papers reserved several keywords -- CTYPEn, CRPIXn,
CRVALn, CDELTn, and CROTAn
-- for use in specifying this relation. While the original paper (Wells, Greisen,
and Harten 1981) defined these keywords only for linear transformations, they
can be also be adapted for non-linear transformations using the definitions in
Section 3.1.1.2. However, for a non-linear
transformation, some keywords in addition to those reserved will be required to
provide a full description.

To create FITS arrays representing the images of objects in the sky
requires projection of the celestial sphere onto the array plane.
The original FITS papers did not specify how this process was to be
carried out. The first approach to this problem, implemented in the
Astronomical Image Processing System (AIPS) and described in AIPS Memo 27
(Greisen 1983), has been widely used, but no conventions have been formally
endorsed by the IAU FITS Working Group. E. Greisen
and M. Calabretta (1996; hereafter GC) have expanded the AIPS approach into
a comprehensive proposal for conventions to be used in projecting
spherical coordinates onto a two-dimensional plane. This proposal has
evolved in response to considerable community discussion and is intended
for formal submission to the IAUFWG. Their proposal discusses a number of
other World Coordinates issues as well.

The remainder of this section (4) will
describe the GC proposal, some other proposed conventions that are gaining acceptance,
and additional FITS community practices. Following these conventions in creating
a data set will make it easier for many others to read and understand the data.
In particular, designers of FITS files that will be distributed outside the
originating site should not adopt conventions that conflict with those described
in this Guide without consulting with other members of the FITS community,
particularly the anticipated readers of the file. In particular, to prevent
confusion, avoid using the keywords and notation of the conventions described
here with different meanings. Because these conventions have not been formally
approved as part of standard FITS, data sets that use other conventions are
not out of conformance. However, these conventions are widely used and have
the best software support; creators of FITS data that use different conventions
will probably need to supply supporting software to their users.